1. Выполните действия: a) \(x^2 \cdot x^9 =\) b) (x^{11} : x^5 =) v) (x^{10} : x^{10} =) г) ((x^8)^5 =) д) ((x^4)^6 \(\cdot\) x^3 =) e) \(\frac{x^{13} \cdot x}{x^{10}} =\) ж) (x^8 \(\cdot\) (x^2)^3 =) з) ((2x)^6 =) и) ((3ab^5)^4 =) к) (\(\frac{a}{4}\)^3 =) л) (\(\frac{4a^3}{3b^7}\)^3 =)

1. Выполняем действия, используя свойства степеней:
a) \(x^2 \cdot x^9 = x^{2+9} = x^{11}\)
б) (x^{11} : x^5 = x^{11-5} = x^6)
в) (x^{10} : x^{10} = x^{10-10} = x^0 = 1)
г) ((x^8)^5 = x^{8 \(\cdot\) 5} = x^{40})
д) ((x^4)^6 \(\cdot\) x^3 = x^{4 \(\cdot\) 6} \(\cdot\) x^3 = x^{24} \(\cdot\) x^3 = x^{24+3} = x^{27})
е) \(\frac{x^{13} \cdot x}{x^{10}} = \frac{x^{13+1}}{x^{10}} = \frac{x^{14}}{x^{10}} = x^{14-10} = x^4\)
ж) (x^8 \(\cdot\) (x^2)^3 = x^8 \(\cdot\) x^{2 \(\cdot\) 3} = x^8 \(\cdot\) x^6 = x^{8+6} = x^{14})
з) ((2x)^6 = 2^6 \(\cdot\) x^6 = 64x^6)
и) ((3ab^5)^4 = 3^4 \(\cdot\) a^4 \(\cdot\) (b^5)^4 = 81a^4b^{5 \(\cdot\) 4} = 81a^4b^{20})
к) (\(\frac{a}{4}\)^3 = \(\frac{a^3}{4^3}\) = \(\frac{a^3}{64}\))
л) (\(\frac{4a^3}{3b^7}\)^3 = \(\frac{(4a^3)^3}{(3b^7)^3}\) = \(\frac{4^3 \cdot (a^3)^3}{3^3 \cdot (b^7)^3}\) = \(\frac{64a^9}{27b^{21}}\))